Energy output prediction method containing fractional derivative partial grey model

Abstract

The invention relates to an energy yield prediction method of a partial grey model containing a fractional derivative, and belongs to the field of energy yield prediction. The method comprises the following steps: firstly, selecting monthly yield current-period values of different energy sources as a database, and constructing an original matrix sequence X (0) as the input of a model; secondly, a fractional order derivative and a fractional order accumulation operator are introduced when the model is constructed, and energy yield prediction is dynamically carried out under the gray action quantity of an exponential function and a sine function; calculating a simulation value X (r) and a reduction value X (0) of the model again, and comparing the simulation value X (r) and the reduction value X (0) with the comparison model on various indexes; a particle swarm optimization algorithm is adopted to find out an optimal parameter vector enabling the MAPE value to be minimum; and finally, applying the new model to energy yield prediction. According to the method, the exponential function and the trigonometric function are introduced, so that the time response function of the model has oscillation characteristics, the volatility of data can be accurately captured and effectively mapped, and the adaptability and the flexibility are remarkably improved; a fractional order derivative and a fractional order accumulation operator are integrated into the model, so that the prediction precision is remarkably improved.

Description

Technical Field

[0001] The invention belongs to the field of energy production prediction, and relates to an energy production prediction method containing a fractional-order derivative partial grey model. Background Art

[0002] The proportion of clean energy needs to be improved, and low-carbon life is still the key to development. In terms of energy supply and demand, my country's energy resources and load centers show reverse distribution characteristics, resulting in more prominent contradictions in energy supply and demand in some regions. During peak periods of energy demand, some regions may face problems such as coal shortages and power shortages. In addition, my country's dependence on foreign crude oil and natural gas is relatively high, and its high dependence on oil and gas imports has become a shortcoming in ensuring energy security. Therefore, scientific and reasonable predictions of energy production in some regions are conducive to timely adjustment of my country's energy structure distribution and supply and demand contradictions.

[0003] The energy production sequence includes not only traditional structured data, but also a large amount of unstructured data. In addition, there is often a strong correlation between energy data. For example, there is a certain substitution relationship between electricity, gas, oil and other energy sources; there is also a certain connection between energy demand and supply in different regions. In addition, the energy production sequence will be affected by uncertain realistic factors such as economy, policy, demand structure and technological innovation, and has the characteristics of a gray system. Under the uncertain background of little data and little information, the gray prediction model achieves the establishment of a prediction model through data processing and phenomenon analysis. It mainly uses differential equations to explore the characteristics of the essence of data and obtain more accurate prediction results. It has the characteristics of simple algorithm, short calculation time and wide application range.

[0004] Reliable and accurate energy production can not only reflect a country's resource endowment and development and utilization capabilities, but also reflect its economic development level, industrial structure, technological progress, and the implementation effect of energy policies. Therefore, scientifically and accurately predicting energy production is of great significance for adjusting the energy structure, promoting the development of clean energy and renewable energy, and reducing dependence on fossil energy. However, energy production forecasting faces many difficulties and challenges. First, it is a heavy task to explore the nonlinearity and complexity of energy production series; second, considering the impact of potential unknown influencing factors in observations on the prediction effect increases the difficulty of improving the prediction accuracy.

[0005] Therefore, a new energy production forecasting method is urgently needed to solve the above problems. Summary of the invention

[0006] In view of this, the purpose of the present invention is to provide an energy production prediction method containing a fractional derivative partial gray model. First, the monthly production values ​​of different energy sources are selected as a database to construct the original matrix sequence X (0)As the input of the model; secondly, fractional derivatives and fractional accumulators are introduced when constructing the model, and energy production is dynamically predicted under the gray action of exponential function and sine function; the simulation value X of the model is calculated again (r) , restore value X (0) And compare with the comparison model in various indicators; use particle swarm optimization algorithm to find the best parameter vector that minimizes the MAPE value; finally, apply the new model to energy production prediction.

[0007] In order to achieve the above object, the present invention provides the following technical solutions:

[0008] A method for predicting energy production using a fractional derivative partial grey model, the method comprising the following steps:

[0009] S1: Select the current monthly output values ​​of different energy sources as the database and construct the original matrix sequence X (0) ;

[0010] S2: According to the original matrix sequence X (0) Calculate the r-order cumulative sequence X (r) , the sequence Z generated by the adjacent mean (r) and the partial derivative sequence

[0011]

[0012] S3: Construct fractional derivative partial differential equation as the whitening equation of grey model CFFPGM(·), introduce fractional derivative operator and fractional accumulation operator into grey model CFFPGM(·), and construct grey action combining exponential function and sine function to describe the oscillation of data;

[0013] S4: According to the r-order cumulative sequence X (r) , the sequence Z generated by the adjacent mean (r) and the partial derivative sequence Construct matrices B and Y, and use the least squares method to estimate the parameter vector of the grey model CFFPGM(·);

[0014] S5: Calculate the simulation value X by time response and cumulative reduction respectively (r) and the restored value X (0) ;

[0015] S6: Calculate the mean square error, mean absolute simulated percentage error, root mean square percentage error, mean absolute error, correlation coefficient and statistical coefficient of the grey model CFFPGM(·) and several comparison models;

[0016] S7: Under the condition of ensuring the best prediction result, the particle swarm algorithm is used to find the optimal parameters with the minimum MAPE value as the goal; the optimal parameters are substituted into the grey model CFFPGM(·) to calculate the simulation value and MAPE value;

[0017] S8: Compare the prediction effects of the grey model CFFPGM(·) with those of the comparison models. If the prediction effect is better than that of all the comparison models, the optimal parameters are saved and used for energy production prediction. Otherwise, the particle swarm algorithm is used to find the optimal parameters.

[0018] Further, in step S1, let X (0) It is a matrix sequence consisting of n m×m matrices constructed as a database with the current values ​​of monthly output of different energy sources:

[0019] X (0) =(X (0) (1),X (0) (2),…,X (0) (n))

[0020] Among them, X (0) (k)(k=1,2,…,n) is an m×m matrix, which is expressed as:

[0021]

[0022] Represents X (0) (k) The value in row i and column j.

[0023] Further, in step S2, the original matrix sequence X (0) r(r∈R + )-order cumulative generation sequence X (r) It is expressed as:

[0024] X (r) =(X (r) (1),X (r) (2),...,X (r) (k),...,X (r) (n))

[0025] In the formula, X (r) (k)(k=1,2,…,n) is an m×m matrix, Represents X (r) (k) The value in row i and column j, where:

[0026]

[0027] and,

[0028]

[0029] where t represents time, Γ(·) represents the gamma function, and Represents X (0) (t) the value in row i and column j;

[0030] Then the sequence Z is generated next to the mean (r) It is expressed as:

[0031] Z (r) =(Z (r) (2),…,Z (r) (n))

[0032] Among them, Z (r) (k)(k=2,3,…,n) is an m×m matrix, Represents Z (r) (k) The value in row i and column j is expressed as:

[0033]

[0034] in,

[0035] Generate sequence Z next to the mean (r) The horizontal and vertical partial derivative sequence Z x (r) and Z y (r) Satisfies the following formula:

[0036]

[0037] express The value in row i and column j, express The value at row i and column j.

[0038] Further, in step S3, the grey model CFFPGM(·) is The abbreviation of is:

[0039]

[0040] Where M represents the number of unknown parameters, M = 3m 2 +8, the whitening equation of the grey model CFFPGM(·) is expressed as:

[0041]

[0042] Among them, (r,α,α 1 )∈(0,1]a,b,c,ω,d are real constant parameter variables, t is X (r) The time variables, x,y are X(r) The spatial variable, α 0 ,β 0 ,β 1 They are m×m order constant matrices, which are expressed as:

[0043]

[0044] In the formula, μ 011 ,μ 012 ,…,μ 0mm ,λ 011 ,λ 012 ,…,λ 0mm ,η 111 ,η 112 ,…,η 1mm is the matrix α 0 ,β 0 ,β 1 All elements in .

[0045] Further, in step S4, first, the grey model The least squares parameter estimate vector of is expressed as:

[0046]

[0047] Its satisfaction Among them, B and Y are matrices constructed according to the above sequence;

[0048] Among them, the matrix B is m 2 (n-1)×(3m 2 +3)-order matrix, which is expressed as:

[0049]

[0050] In matrix B, yes The value at row i, column j; and

[0051]

[0052] The constructed matrix Y is m 2 The (n-1)×1 matrix is ​​expressed as:

[0053]

[0054] In the matrix Y, Yes X (r) (k) The value in row i and column j.

[0055] Further, in step S5, the grey model The time response is:

[0056]

[0057] in, for Simulated values ​​of the model The value in row i and column j;

[0058] Gray Model The final reduction formula is:

[0059]

[0060] in, for The restored value of the model The value at coordinate (r,c);

[0061] Further, in step S6, the comparison models include ARGM (1,1), EPGM (2,1,τ), NGM (1,1), TDGM (1,1), LSTM and ARIMA models. And all compared models, there are:

[0062] The calculation formula for mean square error MSE is:

[0063]

[0064] The calculation formula for the mean absolute simulation percentage error MAPE is:

[0065]

[0066] The calculation formula for the root mean square percentage error RMSPE is:

[0067]

[0068] The calculation formula for the mean absolute error MAE is:

[0069]

[0070] The calculation formula of the correlation coefficient R is:

[0071]

[0072] Where cov(·) represents covariance and Var(·) represents variance.

[0073] The calculation formula of the statistical coefficient U1 is:

[0074]

[0075] The calculation formula of the statistical coefficient U2 is:

[0076]

[0077] in, Corresponding to the grey model and the original matrix sequence and model-reduced value matrix sequence in all compared models.

[0078] Further, in step S7, with the goal of minimizing the average relative error, the relationship between model parameters and the range of parameter values ​​are considered, and the following nonlinear optimization model is established:

[0079]

[0080]

[0081]

[0082] The particle swarm optimization algorithm is used to optimize the optimization model and obtain the optimal fractional order r, the parameters ω and d in the sine function, and the parameters α and α in the exponential function. 1 .

[0083] Further, in step S8, the optimal parameters are substituted into Various indicators are calculated in the model and compared with the indicator values ​​of the comparison model. If the error range is met and the correlation coefficient R value of the new model is higher than that of all comparison models and other indicators are lower than that of all comparison models, the new model will be applied to energy production prediction; otherwise, the particle swarm algorithm will continue to be used to find the optimal parameters.

[0084] The beneficial effects of the present invention are:

[0085] The present invention innovates on the basis of the traditional gray prediction model, constructs a gray prediction model based on fractional-order accumulation operators and fractional-order derivative operators, and constructs a gray action with a combination of exponential functions and sine function terms. This model introduces exponential functions and trigonometric functions, so that the time response function of the model has an oscillating characteristic, so that it can accurately capture and effectively map the volatility of the data, significantly improving the adaptability and flexibility of the model. In addition, in order to further enhance the predictive performance of the model, fractional-order derivatives and fractional-order accumulation operators are also cleverly integrated into the new model. This not only enriches the theoretical framework of the model, but also significantly improves the prediction accuracy in practical applications, providing a solid and reliable tool support for data analysis and prediction in the field of energy production.

[0086] Other advantages, objectives and features of the present invention will be described in the following description to some extent, and to some extent, will be obvious to those skilled in the art based on the following examination and study, or can be taught from the practice of the present invention. The objectives and other advantages of the present invention can be realized and obtained through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0087] In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention will be described in detail below in conjunction with the accompanying drawings, wherein:

[0088] Figure 1 It is an overall flow chart of an energy production prediction method containing a fractional derivative partial grey model of the present invention;

[0089] Figure 2 It is a comparison chart of the overall fitting trend of the gray-biased model of the present invention and other comparative models;

[0090] Figure 3 It is an APE comparison diagram of the grayish model of the present invention and other comparison models. DETAILED DESCRIPTION

[0091] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments only illustrate the basic concept of the present invention in a schematic manner, and the following embodiments and features in the embodiments can be combined with each other without conflict.

[0092] Among them, the drawings are only used for illustrative explanations, and they only represent schematic diagrams rather than actual pictures, and should not be understood as limitations on the present invention. In order to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of actual products. For those skilled in the art, it is understandable that some well-known structures and their descriptions in the drawings may be omitted.

[0093] The same or similar numbers in the drawings of the embodiments of the present invention correspond to the same or similar parts; in the description of the present invention, it should be understood that if the terms "upper", "lower", "left", "right", "front", "rear", etc. indicate the orientation or position relationship, they are based on the orientation or position relationship shown in the drawings, which is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, the terms describing the position relationship in the drawings are only used for illustrative purposes and cannot be understood as limiting the present invention. For ordinary technicians in this field, the specific meanings of the above terms can be understood according to specific circumstances.

[0094] See also Figure 1 to Figure 3 , which is an energy production prediction method based on a fractional derivative partial grey model.

[0095] The present invention provides an energy production prediction method including a fractional derivative gray model. Figure 1 As shown, the method specifically comprises the following steps:

[0096] S1: Select the current monthly output values ​​of different energy sources as the database and construct the original matrix sequence X (0) As input to the model;

[0097] S2: Process the original sequence and calculate the r-order cumulative sequence X (r) , the sequence Z is generated next to the mean (r) and the partial derivative sequence

[0098] S3: Constructing fractional derivative partial differential equations as models In order to improve the prediction accuracy of the model, the fractional derivative operator and the fractional accumulation operator are introduced into the model, and the grey action combining the exponential function and the sine function is constructed to describe the oscillation of the data.

[0099] S4: Use the above sequence to construct matrices B and Y, and use the least squares method to estimate the parameter vector;

[0100] S5: Calculate the simulation value X by time response and cumulative reduction respectively (r) and the restored value X (0) ;

[0101] S6: Computational Model The mean square error, mean absolute simulated percentage error, root mean square percentage error, mean absolute error, correlation coefficient and statistical coefficient of the six comparison models ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM and ARIMA models are shown in Table 1.

[0102] S7: Use the particle swarm algorithm to find the optimal parameters that minimize the MAPE value while ensuring the optimal prediction results; substitute the optimal parameters into Calculate simulation values ​​and MAPE values ​​in the model;

[0103] S8: If the error range is met and the prediction effect of the new model is better, that is, the R value of the new model is higher than that of the comparison model, and the values ​​of the other six indicators are lower than those of the comparison model, then the new model can be applied to energy production prediction. Otherwise, the particle swarm algorithm will continue to be used to find the optimal parameters.

[0104] In step S1 of this embodiment, let X (0) It is a matrix sequence consisting of n m×m matrices constructed as a database with the current values ​​of monthly output of different energy sources:

[0105] X (0) =(X (0) (1),X (0) (2),…,X (0) (n))

[0106] Among them, X (0) (k)(k=1,2,…,n) is an m×m matrix, which is expressed as:

[0107]

[0108] Represents X (0) (k) The value in row i and column j.

[0109] In step S2 of this embodiment, the original sequence is processed to calculate the r-order cumulative sequence X (r) , the sequence Z is generated next to the mean (r) and the partial derivative sequence Specifically include: X (r) (k) is X (0) (k) r(r∈R + )-order cumulative generation sequence:

[0110] X (r) =(X (r) (1),X (r) (2),...,X (r) (k),...,X (r) (n))

[0111] Among them, X (r) (k)(k=1,2,…,n) is an m×m matrix, Represents X (r) (k) The value in row i and column j is as follows:

[0112]

[0113] and:

[0114]

[0115] where t represents time, Γ(·) represents the gamma function, and Represents X (0) (t) The value at row i and column j.

[0116] Generate sequence Z next to the mean (r) It is expressed as:

[0117] Z (r) =(Z (r) (2),…,Z (r) (n))

[0118] Among them, Z (r) (k)(k=2,3,…,n) is an m×m matrix, Represents Z (r) (k) the value in row i, column j, and The details are as follows:

[0119]

[0120] Generate sequence Z next to the mean (r) The horizontal and vertical partial derivative sequence Z x (r) and Z y (r) Satisfies the following formula:

[0121]

[0122]

[0123] express The value in row i and column j, express The value at row i and column j.

[0124] In step S3 of this embodiment, The expression is:

[0125]

[0126] Where M = 3m 2 +8, k=2,3,…,n; and its whitening equation is expressed as:

[0127]

[0128] Among them, (r,α,α1 )∈(0,1]a,b,c,ω,d are real constant parameter variables, t is X (r) The time variables, x,y are X (r) The spatial variable, α 0 ,β 0 ,β 1 They are m×m-order constant matrices, as follows:

[0129]

[0130] μ 011 ,μ 012 ,…,μ 0mm ,λ 011 ,λ 012 ,…,λ 0mm ,η 111 ,η 112 ,…,η 1mm is the matrix α 0 ,β 0 ,β 1 All elements in .

[0131] In step S4 of this embodiment, the above sequence is used to construct a matrix, and the parameter vector is estimated using the least squares method, which specifically includes: model, least squares parameter estimates vector

[0132]

[0133] satisfy:

[0134] Where the matrix B is m 2 (n-1)×(3m 2 +3)-order matrix, which is expressed as:

[0135]

[0136] In matrix B, yes The value at row i, column j; and

[0137]

[0138] The constructed matrix Y is m 2 The (n-1)×1 matrix is ​​expressed as:

[0139]

[0140] In the matrix Y, Yes X (r) (k) The value in row i and column j.

[0141] In step S5 of this embodiment, the grey model The time response is:

[0142]

[0143] in, for Simulated values ​​of the model The value in row i and column j;

[0144] Gray Model The final reduction formula is:

[0145]

[0146] in, for The restored value of the model The value at coordinate (i,j).

[0147] In step S6 of this embodiment, the model The formulas of mean square error, mean absolute simulated percentage error, root mean square percentage error, mean absolute error, correlation coefficient and statistical coefficient of the six comparison models ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM and ARIMA models are shown in Table 1.

[0148] Table 1

[0149]

[0150]

[0151] The smaller the MSE, MAPE, RMSPE, MAE, U1, and U2 index values ​​are, the higher the model accuracy is. The closer the R value is to 1, the better the model effect is.

[0152] In step S7 of this embodiment, the particle swarm algorithm is used to find the optimal parameters that minimize the MAPE value while ensuring the optimal prediction result; the optimal parameters are substituted into The simulation value and MAPE value are calculated in the model, and the process is as follows:

[0153] With the goal of minimizing the average relative error, considering the relationship between model parameters and the range of parameter values, the following nonlinear optimization model is established:

[0154]

[0155]

[0156] The particle swarm optimization algorithm is used to optimize the optimization model and obtain the optimal fractional order r, the parameters ω and d in the sine function, and the parameters α and α in the exponential function. 1 .

[0157] In step S8 of this embodiment, the optimal parameters are substituted into Each index is calculated in the model and compared with the seven index values ​​of the six comparison models. If the error range is met and the prediction effect of the new model is better, the new model can be applied to energy production forecasting.

[0158] This example applies the model to the production of raw coal and gasoline in three provinces in China, as well as the production of two clean energy sources, coalbed methane in Shanxi and natural gas in Qinghai, to illustrate the effectiveness of the model from different perspectives. With the help of a comprehensive analysis of seven evaluation indicators, the results show that the simulation and prediction accuracy of the model is significantly better than the other six comparative prediction models, reflecting the superior ability of the new model in predicting the production of different types of energy in different regions.

[0159] This embodiment compares the prediction model of the present invention with other models. The trend comparison diagram of the prediction model of the present invention and other models is shown in FIG. Figure 2 As shown in the APE comparison chart Figure 3 As shown. The data of this case is selected from the coalbed methane energy production data of Shanxi Province. The data comes from the monthly production value data of energy in various provinces in China from the National Bureau of Statistics (https: / / data.stats.gov.cn / ). Since there is no data on the production in some months, and there is no regularity in the months without data, the data has the characteristics of incomplete information. This small sample and incomplete information characteristics are in line with the scope of gray system theory research. 20 coalbed methane production data from May to December 2021, March to December 2022, and March to April 2023 in Shanxi Province are selected. A 2×2 matrix is ​​established for every 4 months of data, and 5 2×2 matrix sequences are constructed. Then the matrix sequence is input into different prediction models for research. The CFFPGM model is still compared with the ARGM(1,1), EPGM(2,1,τ), NGM(1,1), TDGM(1,1), LSTM and ARIMA models. In this embodiment, the ARIMA model structure calculated based on the original data is the ARIMA (1,0,1) model, and the optimal parameter vector of the CFFPGM model is (r, α, d, ω, α 1 )=(0.7388,0.0067,584.7848,431.0233,160.2397), the optimal parameter vector of the EPGM model is (τ,r 1 ,r 2)=(1.0000,1.0000,1.0000). The seven models are simulated and compared. The evaluation index calculation results of the seven models are shown in Table 2.

[0160] Table 2

[0161]

[0162] As can be seen from Table 2, the MAPE value of the CFFPGM model is only 1.3992%, while the other comparison models are all greater than 2.5%, and the other 6 indicators of the CFFPGM model are also the best. The maximum value of the evaluation index R is 1. The larger the R value, the higher the accuracy of the model. The R value of the CFFPGM model is 0.9535, which is the largest among the comparison models. Therefore, the effectiveness of the CFFPGM model can be explained. In addition, as can be seen from Table 2, the overall simulation effect of the traditional statistical method ARIMA and the neural network model LSTM is poor, and the improved partial gray model CFFPGM is better than ARIMA and LSTM. This shows that partial gray models can not only be applied to situations with large sample sizes, but more importantly, they perform better than time series models and neural network models that usually require a large number of training data sets.

[0163] In order to more intuitively demonstrate the effectiveness of the CFFPGM model, the above results are visualized. Figure 2 , APE comparison chart see Figure 3 .like Figure 2 As shown, the new model is closest to the original data and has the highest degree of overlap compared with other models, while other models are farthest from the original data. Figure 3 The APE box plot in the figure shows that the CFFPGM model has the smallest mean, the shortest box, relatively concentrated data, and the smallest degree of dispersion, followed by the TDGM model and the ARIMA model. The ARGM model, EPGM model, NGM model, and LSTM model have relatively poor results. Therefore, the new model CFFPGM has the highest fitting accuracy.

[0164] Secondly, from Figure 2 The trend graph in further shows that the FPGM proposed in the present invention is superior to other grey prediction models, such as the ARGM model, the EPGM model, the NGM model, the TDGM model, as well as statistical methods and neural networks, in predicting non-periodic oscillatory data. This fact proves the effectiveness of the method of introducing fractional derivative operators and fractional cumulative operators as well as exponential function terms and sine function grey actions in the model. The particle swarm algorithm is used to optimize the model parameters, so that the new model can more accurately predict non-monotonic oscillatory data.

[0165] In summary, the CFFPGM model processes energy production data in the form of matrix sequences, increases the sample size, and the exponential function terms and trigonometric function terms in the model can effectively capture the changing trend and oscillation of the data. In addition, the use of fractional-order accumulation operators and fractional-order derivatives can also make the model have higher fitting accuracy. This model can accurately provide a method for energy production prediction, has a certain theoretical basis and use value, and performs well in the prediction task of China's energy production.

[0166] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution, which should be included in the scope of the claims of the present invention.

Claims

1. An energy production prediction method containing a fractional derivative partial grey model, characterized by: The method comprises the following steps: S1: Select the current monthly output values ​​of different energy sources as the database and construct the original matrix sequence X (0) ; S2: According to the original matrix sequence X (0) Calculate the r-order cumulative sequence X (r) , the sequence Z generated by the adjacent mean (r) and the partial derivative sequence S3: Construct fractional derivative partial differential equation as the whitening equation of grey model CFFPGM(·), introduce fractional derivative operator and fractional accumulation operator into grey model CFFPGM(·), and construct grey action combining exponential function and sine function to describe the oscillation of data; S4: According to the r-order cumulative sequence X (r) , the sequence Z generated by the adjacent mean (r) and the partial derivative sequence Construct matrices B and Y, and use the least squares method to estimate the parameter vector of the grey model CFFPGM(·); S5: Calculate the simulation value X by time response and cumulative reduction respectively (r) and the restored value X (0) ; S6: Calculate the mean square error, mean absolute simulated percentage error, root mean square percentage error, mean absolute error, correlation coefficient and statistical coefficient of the grey model CFFPGM(·) and several comparison models; S7: Under the condition of ensuring the best prediction result, the particle swarm algorithm is used to find the optimal parameters with the minimum MAPE value as the goal; the optimal parameters are substituted into the grey model CFFPGM(·) to calculate the simulation value and MAPE value; S8: Compare the prediction effects of the grey model CFFPGM(·) with those of the comparison models. If the prediction effect is better than that of all the comparison models, the optimal parameters are saved and used for energy production prediction. Otherwise, the particle swarm algorithm is used to find the optimal parameters.

2. The energy production prediction method containing the fractional derivative partial grey model according to claim 1 is characterized by: In step S1, let X (0) It is a matrix sequence consisting of n m×m matrices constructed as a database with the current values ​​of monthly output of different energy sources: X (0) =(X (0) (1),X (0) (2),…,X (0) (n)) Among them, X (0) (k), k = 1, 2, ..., n is an m × m matrix, which is expressed as: Represents X (0) (k) The value in row i and column j, where i, j = 1, 2, …, m, k = 1, 2, …, n.

3. The energy production prediction method containing the fractional derivative partial gray model according to claim 2 is characterized by: In step S2, the original matrix sequence X (0) r(r∈R + )-order cumulative generation sequence X (r) It is expressed as: X (r) =(X (r) (1),X (r) (2),...,X (r) (k),...,X (r) (n)) Where, X (r) (k), k=1,2,…,n is an m×m matrix, Represents X (r) (k) The value in row i and column j, i,j = 1,2,…,m,k = 1,2,…,n, where: and, Where t represents time, Γ(·) represents the gamma function, and Represents X (0) (t) The value in row i and column j; Then the sequence Z is generated next to the mean (r) It is expressed as: WITH (r) =(From (r) (2),…,From (r) (n)) Among them, Z (r) (k), k = 2, 3, ..., n is an m × m matrix, Represents Z (r) (k) The value in row i and column j, i, j = 1, 2, ..., m; k = 2, 3, ..., n, which is expressed as: in, Generate sequence Z next to the mean (r) The horizontal and vertical partial derivative sequence Z x (r) and Z y (r) Satisfies the following formula: express The value in row i and column j, express The value in row i and column j is: i, j = 1, 2, …, m; k = 1, 2, …, n.

4. The energy production prediction method containing the fractional derivative partial grey model according to claim 3 is characterized by: In step S3, the grey model CFFPGM(·) is The abbreviation of is: In the formula, M in the model represents the number of unknown parameters, and M = 3m 2 +8, the whitening equation of the grey model CFFPGM(·) is expressed as: Among them, (r, α, α1) ∈ (0, 1], a, b, c, ω, d are real constant parameter variables, t is X (r) The time variables, x,y are X (r) The spatial variables of , α0, β0, β1 are m×m order constant matrices, which are expressed as: In the formula, μ 011 ,μ 012 ,…,μ 0mm ,λ 011 ,λ 012 ,…,λ 0mm ,η 111 ,η 112 ,…,η 1mm are all the elements in the matrices α0,β0,β1.

5. The energy production prediction method containing the fractional derivative partial grey model according to claim 4 is characterized by: In step S4, first, the grey model The least squares parameter estimate vector of is expressed as: Its satisfaction Among them, B and Y are matrices constructed according to the above sequence; Among them, the matrix B is m 2 (n-1)×(3m 2 +3)-order matrix, which is expressed as: In matrix B, yes The value at row i, column j; and The constructed matrix Y is m 2 The (n-1)×1 matrix is ​​expressed as: In the matrix Y, Yes X (r) (k) The value in row i and column j.

6. The energy production prediction method containing the fractional derivative partial grey model according to claim 5 is characterized by: In step S5, the grey model The time response is: i,j=1,2,...,m;k=1,2,...,n-1 in, for Simulated values ​​of the model The value in row i and column j; Gray Model The final reduction formula is: in, for The restored value of the model The value at coordinate (i,j).

7. The energy production prediction method containing fractional derivative partial grey model according to claim 6 is characterized by: In step S6, the comparison models include ARGM (1,1), EPGM (2,1,τ), NGM (1,1), TDGM (1,1), LSTM and ARIMA models. And all compared models, there are: The calculation formula for mean square error MSE is: The calculation formula for the mean absolute simulation percentage error MAPE is: The calculation formula for the root mean square percentage error RMSPE is: The calculation formula for the mean absolute error MAE is: The calculation formula of the correlation coefficient R is: In the formula, cov(·) represents covariance, Var(·) represents variance; The calculation formula of the statistical coefficient U1 is: The calculation formula of the statistical coefficient U2 is: Among them, X (0) (k), Corresponding to the grey model and the original matrix sequence and model-reduced value matrix sequence in all compared models.

8. The energy production prediction method containing the fractional derivative partial grey model according to claim 7 is characterized by: In step S7, with the goal of minimizing the average relative error, the following nonlinear optimization model is established by considering the relationship between model parameters and the range of parameter values: i,j=1,2,...,m,k=1,2,...,n-1 The optimization model is optimized by using the particle swarm optimization algorithm to obtain the optimal fractional order r, the parameters ω and d in the sine function, and the parameters α and α1 in the exponential function.

9. The energy production prediction method containing fractional derivative partial grey model according to claim 8 is characterized by: In step S8, the optimal parameters are substituted into Various indicators are calculated in the model and compared with the indicator values ​​of the comparison model. If the error range is met and the correlation coefficient R value of the new model is higher than that of all comparison models and other indicators are lower than that of all comparison models, the new model will be applied to energy production prediction; otherwise, the particle swarm algorithm will continue to be used to find the optimal parameters.

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